The chain, owned by the billionaire entrepreneur Phillip Green, does not currently advertise above the line, instead relying on in-store promotion.
Green bought Bhs four years ago from the Storehouse Group and has been credited with transforming the company since the departure of Sir Terence Conran from the Storehouse Group in 1990. He is now thought to be looking to boost its profile to compete with close rivals, including Marks & Spencer and Debenhams.
DFGW created advertising for Bhs back in 1999, after prising the account from Saatchi & Saatchi. The £1.5 million integrated campaign included a TV ad, which carried the endline: "Wild at heart."
News of the discussions coincides with Green's expansion of Bhs outlets to Eastern Europe. The first store opened in Lithuania in January, with a second proposed for Moscow.
Green also controls Acardia, which owns Topshop and Dorothy Perkins.
He recently failed in an attempt to add Harrods to his empire.
A spokeswoman for Bhs said: "We currently have no commitments with regards to media and advertising campaigns. However, this does not prevent us from reviewing this area, nor any future opportunities that we may or may not wish to pursue."